A Strategic Design Route to Find a Depleted Uranium High-Entropy Alloy with Great Strength

Abstract

The empirical parameters of mixing enthalpy (ΔH_mix), mixing entropy (ΔS_mix), atomic radius difference (δ), valence electron concentration (VEC), etc., are used in this study to design a depleted uranium high-entropy alloy (HEA). X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were used to assess the phase composition. Compression and hardness tests were conducted to select alloy constituents with outstanding mechanical properties. Based on the experimental results, the empirical criteria of HEAs are an effective means to develop depleted uranium high-entropy alloys (DUHEAs). Finally, we created UNb_0.5Zr_0.5Mo_0.5 and UNb_0.5Zr_0.5Ti_0.2Mo_0.2 HEAs with outstanding all-round characteristics. Both alloys were composed of a single BCC structure. The hardness and strength of UNb_0.5Zr_0.5Mo_0.5 and UNb_0.5Zr_0.5Ti_0.2Mo_0.2 were 305 HB and 1452 MPa, and 297 HB and 1157 MPa, respectively.

1. Introduction

The concept of high-entropy alloys (HEAs) offers a new approach to exploring materials, expanding the research scope and the compositional palette. Due to the high entropy effect, HEAs can form a simple solid solution structure with excellent properties under a high concentration of multiple components [1]. HEAs with high strength and toughness [2,3], stability at high temperatures [4,5], and corrosion resistance [4,6] have been investigated. The HEA system mainly focuses on the 3rd to 5th period, 3d electron layer elements, and other main group elements, which usually form face-centered cubic (FCC) and body-centered-cubic (BCC) structures. Meanwhile, the rare earth elements, such as Tb, Dy, Lu, Tm, and Ho, usually form a hexagonal-close-packed (HCP) structure [7,8].

Unlike uranium, depleted uranium (DU) has very little radioactivity and is often used in military applications because of its self-sharpening properties and high density [9,10,11]. There are three structures of U (

Table 1. Uranium allotropes and their characteristics, data from [17,18].

Allotrope	α-U	β-U	γ-U
Temperature (°C)	<667.7	667.7~774.8	774.8~1132.3
Crystal structure
Density (g/cm3)	19.05	18.13	17.91

), and the γ-U structure with a BCC structure has ideal symmetry and properties at high temperatures. Alloying elements Zr [12], Ti [11,13], Mo [14], Nb [15,16], amongst others, usually have a wide range of solubility in γ-U of the BCC structure. Zr and Nb can dissolve completely with U and form the γ-phase at high temperatures. Ti can dissolve in the U matrix and form the γ-phase at a temperature above 725 °C, and the maximum solubility of Mo in γ-U is 21.2 weight percent (wt.%). HEAs have superior properties to traditional alloys. By applying the concept of high entropy to DU alloys and taking full advantage of γ-U, we can design DUHEAs with excellent performance and provide more options for high-performance structural materials.

2. Design Idea and Experimental Route for DUHEAs

2.1. Design Idea

HEAs design commonly includes high-throughput preparation, CALPHAD (phase diagram calculation) [19,20], and DFT (density functional theory) [21,22,23]. Generally, the factors considered in the calculation and simulation are ideal and are insufficient to reflect the actual casting process. In this study, we combined the solid solution formation criteria of HEA with an experimental search for high-performance DUHEAs. The elements Nb, Mo, Ti, and Zr, which have significant solubility in U, were selected. The physical properties are listed in

Table 2. Physical properties of each element, data from [24,25,26].

Element	U238	Nb	Zr	Ti	Mo
Atomic number	92	41	40	22	42
Atomic radius (pm)	139	143	159	146	141
Density (g/cm3)	19.05	8.52	6.49	4.51	10.20
Melting point (K)	1405	2750	2128	1941	2896
Electronegativity	1.38	1.60	1.33	1.54	2.16
Lattice content (pm)	343.3	330.1	360.9	327.6	314.7
Valence electron concentration (VEC)	3	5	4	4	6

.

Yeh et al. [27] believe that the mixing entropy (ΔS_mix) is the main factor promoting the formation of solid solutions in HEAs. Zhang [28] extended the Hume-Rothery criterion to HEAs and proposed δ, ΔH_mix, and Ω as the factors affecting the formation of HEA solid solution phases.

The mixing entropy can be calculated by the following Formula [1]:

$$\Delta S_{mix}=-R{\displaystyle \sum }_{i=1}^n\left(c_i\ln c_i\right)$$

(1)

where R is the ideal gas constant (J·mol⁻¹·K⁻¹); n is the number of components in the alloy; and c_i is the atomic fraction of the ith component in the alloy. From Formula (1), ΔS_mix reaches the maximum when the atomic ratio of the elements in the alloy is equal. In general, alloys are assigned to the class of HEAs when the mixing entropy is higher than 1.5 R [29].

The parameter, δ, for the difference in atomic radius can be expressed as follows [1]:

$$\mathsf{\delta }=\sqrt{{\displaystyle \sum }_{i=1}^n{c}_i{\left(1-\frac{r_i}{\overline{r}}\right)}^2}$$

(2)

$$\overline{r}={{\displaystyle \sum }}_{i=1}^n{c}_i{r}_i$$

(3)

where $\overline{r}$ is the average atomic radius of the alloy (Å), and r_i is the atomic radius of the ith element of the alloy (Å).

The mixing enthalpy of a multi-component alloy can be calculated by the following formula [1]:

$$\Delta H_{mix}={\displaystyle \sum }_{i=1,i\ne j}^{n}4H_{AB}^{mix}{c}_i{c}_j$$

(4)

where $H_{AB}^{mix}$ is the mixing enthalpy of the ith and jth elements (kJ·mol⁻¹); c_i is the atomic percentage of the ith element in the alloy; and c_j is the atomic percentage of the jth elements in the alloy. The mixing enthalpy among U, Nb, Zr, Ti, and Mo are listed in

Table 3. Mixing enthalpy between elements, data from [24,25,26] ($H_{AB}^{mix}$, kJ/mol).

	U	Nb	Zr	Ti	Mo
U	-	4	−3	0	2
Nb	-	-	4	2	−6
Zr	-	-	-	0	−6
Ti	-	-	-	-	−4
Mo	-	-	-	-	-

.

To simplify the prediction standard of an HEA solid solution structure, Zhang [30] proposed the Ω parameter, the definition of which is expressed as follows [1]:

$$\Omega =\frac{T_m\Delta S_{mix}}{\left|\Delta H_{mix}\right|}$$

(5)

where T_m is the melting point of a multi-component alloy (K); ΔS_mix is the mixing entropy of a multi-component alloy (J·K⁻¹·mol⁻¹); and ΔH_mix is the mixing enthalpy of a multi-component alloy (J·K⁻¹·mol⁻¹).

To develop DUHEAs with excellent mechanical properties, Zr and Nb, which can dissolve indefinitely with γ-U at a high temperature to form a BCC solid solution structure, were added to the DU ternary alloy. Then, Ti and Mo were added to the DU ternary alloy to refine its properties. The study path is shown in Figure 1.

2.2. Test Method

Ingots with a mass of approximately 50 g were prepared using a Vacuum arc melting furnace and pure metals of U, Nb, Mo, Ti, and Zr (purity was higher than 99 wt.%). To ensure chemical homogeneity, the ingots were re-melted at least 4~5 times. An X-ray diffractometer (XRD, Bruker D8 Advance, Bruker AXS, Bruker AXS, Karlsruhe, Germany), with Cu Kα radiation, was used to measure the phase composition of the alloys. The scanning range was from 15° to 90°, and the scanning speed was 5°/min. The micro-morphologies of the alloys were observed by scanning electron microscopy (SEM, EVO18, Carl Zeiss AG, Jena, Germany) operating at 20 keV. The chemical composition was observed by energy-dispersive spectroscopy (EDS) equipped in the SEM. The standard bright-field (BF), image, and selected area electron diffraction (SAED) patterns were obtained by transmission electron microscope (TEM, Tecnai F30, FEI, Hillsboro, OR, USA) operating at 300 kV, and the TEM data were processed using the Digital Micrograph software. Hardness of the alloys was measured using the Wilson Brinell hardness meter BH3000 (Wilson, Norwood, MA, USA) under a load of 1840 N for 10 s. Room temperature compression tests were carried out by CMT5105 (Suns, Shenzhen, China). The specimen was a Φ 6 mm cylinder with a height-to-diameter ratio of between 1.5 and 2. The compression tests were performed at a compression rate of 10⁻³ s⁻¹.

3. Design Process and Experimental Results

3.1. Ternary U-Nb-Zr Medium-Entropy Alloy (MEA)

Firstly, the U-Nb-Zr alloy system was studied. The thermodynamic parameters of the alloy system are listed in

Table 4. Thermodynamic parameters of the U-Nb-Zr alloy system.

Alloys	δ (%)	ΔHmix (KJ/mol)	ΔSmix (KJ/mol)	Tm (K)	Ω	VEC
UNbZr	5.88	2.22	9.13	2094	8.6	4.00
UNb0.5Zr	6.26	0.64	8.77	1963	26.9	3.80
UNbZr0.5	5.13	2.88	8.77	2087	6.4	4.00
UNb0.5Zr0.5	5.69	1.50	8.64	1922	11.1	3.75
UNb1.5Zr	5.55	2.94	8.97	2188	6.7	4.14
UNbZr1.5	6.08	1.80	8.97	2099	10.5	4.00

, and the relationship between δ-ΔH and δ-Ω of the alloy is shown in Figure 2. Zr and Nb are infinitely soluble in U, indicating that the alloy system has a strong tendency to form solid solutions. From Figure 2a all alloys had a disordered solid solution phase. While in Figure 2b, UNbZr0.5 and UNb1.5Zr are in the solid solution and intermetallic compound zones, UNbZr is on the boundary of the solid solution and intermetallic compound zones, which does not tend to form a solid solution. The value of VEC for every alloy was lower than 6.87, forming a stable BCC solid solution structure [31]. The results show that the alloys have a disordered solution phase.

The XRD pattern of the medium entropy alloys are presented in Figure 3. Regardless of the uranium oxides, the phase compositions of the alloys were almost identical and were composed of a single BCC phase. In addition, the diffraction peaks appeared to shift with the change in Nb and Zr contents. Combining Bragg’s Law with $d_{hkl}=\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$\sqrt{h^2+k^2+l^2}$}\right.$ (d_hkl is the interplanar spacing), the diffraction peaks shifted suggesting lattice content changes [32]. Because U, Nb, and Zr have different lattice constants, the variation of the lattice constants of the alloys is complex. According to the electron diffraction of the UNbZr alloy in Figure 4a,b, the alloy exhibited a single-phase BCC structure, which is consistent with the prediction of the alloy formation.

The microstructures of the medium-entropy alloys in the U-Nb-Zr system are shown in Figure 5. The microstructure of UNbZr is presented in Figure 5a. The light-colored region was a U-enriched interdendritic structure, while Zr and Nb formed the BCC dendritic structure of the primary phase due to their higher melting points. When the Nb content decreased, as shown in Figure 5b, the segregation of UNb_0.5Zr was more pronounced than that of UNbZr. When the Zr content decreased, the segregation of UNbZr_0.5 decreased, as shown in Figure 5c, and the dendrite structure become finer. In Figure 5d,e, the alloy compositions of UNb_0.5Zr_0.5 and UNb_1.5Zr are uniform. The structure of the UNbZr_1.5 alloy is shown in Figure 5e, which was similar to UNbZr and displayed a typical as-cast dendrite structure (uniform region) with segregation of the components (U-enriched region).

The hardness and yield strength of the alloys of the U-Nb-Zr system are given in

Table 5. Hardness and strength of the U-Nb-Zr alloy system.

Properties	UNb0.5Zr0.5	UNb0.5Zr	UNbZr0.5	UNbZr	UNb1.5Zr	UNbZr1.5
Hardness (HB)	246	263	211	235	243	238
Strength (MPa)	793	883	748	863	858	755

. The hardness and strength of UNbZr_0.5 and UNbZr_1.5 were lower than those of other alloys. It seems that the mechanical properties of UNb_0.5Zr, UNbZr, and UNb_1.5Zr were higher than those of UNb_0.5Zr_0.5. In particular, the organization of UNb_0.5Zr was more homogeneous than that of UNb_0.5Zr_0.5 (see Figure 5). However, this study aimed to utilize waste DU and improve its potential availability; therefore, UNb_0.5Zr_0.5 was selected as the base alloy for the subsequent work.

3.2. Quaternary U-Nb-Zr-X HEA

From the microstructural study of the U-Nb-Zr ternary alloys, the elemental distribution of the UNb_0.5Zr_0.5 alloy is the most uniform, the segregation phenomenon was not obvious, and its comprehensive mechanical properties were excellent.

Table 6. Thermodynamic parameters of UNb_0.5Zr_0.5-X HEAs.

Alloys	δ (%)	ΔHmix (KJ/mol)	ΔSmix (KJ/mol)	Tm (K)	Ω	VEC
UNb0.5Zr0.5Ti0.2	5.42	1.40	10.39	1924	14.3	3.77
UNb0.5Zr0.5Ti0.5	5.09	1.28	11.07	1926	16.7	3.80
UNb0.5Zr0.5Ti	4.64	1.11	11.05	1928	19.2	3.83
UNb0.5Zr0.5Mo0.2	5.49	0.58	10.39	2011	36.1	3.95
UNb0.5Zr0.5Mo0.5	5.23	−0.32	11.07	2117	73.3	4.20
UNb0.5Zr0.5Mo	4.87	−1.11	11.05	2247	22.4	4.50

shows the thermodynamic parameters of UNb_0.5Zr_0.5-X (Ti/Mo) HEAs. From the relationship diagram of δ-ΔH and δ-Ω in Figure 6, the studied UNb_0.5Zr_0.5-X (Ti/Mo) HEAs were solid solution phases. Based on their VEC, it was discovered that these alloys were BCC phases.

The XRD results of UNb_0.5Zr_0.5-X (Ti/Mo) HEAs presenting BCC structures are represented in Figure 7. Ignoring the uranium oxides, most of the alloys consisted of a single BCC structure, UNb_0.5Zr_0.5Ti and UNb_0.5Zr_0.5Mo HEAs forming two BCC structures. The diffraction peak changed to a higher angle as the concentrations of Ti and Mo grew, showing that the lattice constant dropped [32]. As presented in Table 2, the lattice contents of U, Mo, and Ti at room temperature are 343.3 pm, 314.7 pm, and 327.6 pm [17,26], respectively. With the addition of Ti and Mo, the lattice constant of the matrix decreased, indicating the occurrence of solid solution and the generation of lattice distortion. When the content of Mo reached the maximum, UNb_0.5Zr_0.5Mo was composed of two BCC structures, which was because Mo has the highest melting point of the elements.

The as-cast microstructures of UNb_0.5Zr_0.5-X (Ti/Mo) HEAs are shown in Figure 8, and the alloys all have a typical as-cast dendritic structure similar to the U-Nb-Zr system alloys. Composition segregation was obvious as the concentration of Ti and Mo increased. UNb_0.5Zr_0.5Ti_0.2, UNb_0.5Zr_0.5Ti_0.5, UNb_0.5Zr_0.5Ti, UNb_0.5Zr_0.5Mo_0.2, and UNb_0.5Zr_0.5Mo_0.5 consisted of a uniform region, a U-enriched region and a UO_x region. Compared with UNb_0.5Zr_0.5Ti_0.2 and UNb_0.5Zr_0.5Ti_0.5, the segregation of the U-enriched region in UNb_0.5Zr_0.5Ti was high obviously. UNb_0.5Zr_0.5Mo was composed of a U-enriched region, Mo-enriched region, and UO_x, which was different from UNb_0.5Zr_0.5Mo_0.2 and UNb_0.5Zr_0.5Mo_0.5. As Figure 8f shows, the Mo-enriched region formed the BCC2 phase that is in line with the XRD patterns of Figure 7.

Table 7. Hardness and strength of the UNb_0.5Zr_0.5-X HEAs.

Properties	UNb0.5Zr0.5Ti0.2	UNb0.5Zr0.5Ti0.5	UNb0.5Zr0.5Ti	UNb0.5Zr0.5Mo0.2	UNb0.5Zr0.5Mo0.5	UNb0.5Zr0.5Mo
Hardness (HB)	233	220	214	289	305	367
Strength (MPa)	760	881	754	/	1452	1668.9 (Crashed)

shows the Brinell hardness and yield strength of the UNb_0.5Zr_0.5-X HEAs. The addition of Ti significantly reduced the hardness of the alloy. When the molar ratio of Ti was 0.5, the yield strength of the alloy reached 881 MPa. While the hardness of the alloy improved dramatically as the Mo percentage increased, the yield strength decreased. This was because the hardness of Mo was higher than that of other elements. In addition, the melting point of Mo was the highest of the five elements, which will improve segregation during the solidification process. As a result, the hardness increased dramatically, and segregation of the alloy increased along with the Mo content, dramatically influencing the mechanical characteristics of the alloy.

3.3. Quinary U-Nb-Zr-Ti-Mo HEAs

We can observe from the previous section on the quaternary HEAs that the proposed alloys could form a stable solid solution phase of a BCC structure. The UNb_0.5Zr_0.5Ti_0.2, UNb_0.5Zr_0.5Ti_0.5, UNb_0.5Zr_0.5Mo_0.2, and UNb_0.5Zr_0.5Mo_0.5 alloys had the most uniform elemental distributions, and the segregation phenomenon was not observed. A five-element DUHEA was prepared by varying the ratio of Ti and Mo and choosing UNb_0.5Zr_0.5Ti_xMo_x.

The thermodynamic properties of Nb-Zr-U-Ti-Mo HEAs are shown in

Table 8. Thermodynamic parameters of U-Nb-Zr-Ti-Mo HEAs.

Alloys	δ (%)	ΔHmix (KJ/mol)	ΔSmix (KJ/mol)	Tm (K)	Ω	VEC
UNb0.5Zr0.5Ti0.2Mo0.2	5.26	0.51	11.91	2005	46.46	3.96
UNb0.5Zr0.5Ti0.5Mo0.5	4.79	−0.44	12.98	2088	60.94	4.17

. The planned UNb_0.5Zr_0.5Ti_xMo_x HEAs were all solid solution phases, as evidenced by the relationship between δ-ΔH and δ-Ω in Figure 9. Based on its VEC, we can predict that the developed alloy will be a BCC phase.

The phase composition and microstructure of the five-element DUHEA were investigated. Figure 10 shows the XRD data on the UNb_0.5Zr_0.5Ti_xMo_x (x = 0.2, 0.5) HEA. UNb_0.5Zr_0.5Ti_0.2Mo_0.2 was composed of a single BCC structure and UNb_0.5Zr_0.5Ti_0.5Mo_0.5 formed two BCC structures. The addition of Ti and Mo contributed to the formation of BCC2. In addition, when the concentration of Ti and Mo increased, the diffraction peaks were shifted to higher angles, indicating a decrease in the lattice constants. Moreover, the diffraction peaks became broader with the increase in the Ti and Mo contents, indicating grain refinement [33].

The as-cast structures of the UNb_0.5Zr_0.5Ti_0.2Mo_0.2 and UNb_0.5Zr_0.5Ti_0.5Mo_0.5 alloys are shown in Figure 11. These alloys had a typical cast dendritic structure of a uniform composition region and U-enriched region between the dendritic structures. It can be observed that the structure segregation phenomenon of the alloys improved as Ti and Mo concentrations increased. This was due to the fact that Mo had a high melting point (higher than U’s melting point) and element redistribution during solidification. The alloy components are equally distributed without noticeable segregation, as seen in the surface scan findings of UNb_0.5Zr_0.5Ti_0.2Mo_0.2 in Figure 12.

The Brinell hardness and yield strength of the UNb_0.5Zr_0.5Ti_xMo_x HEAs are listed in

Table 9. Hardness and strength of the UNb_0.5Zr_0.5Ti_xMo_x HEAs.

Properties	UNb0.5Zr0.5Ti0.2Mo0.2	UNb0.5Zr0.5Ti0.5Mo0.5
Hardness (HB)	297	350
Strength (MPa)	1157	1215 (Crashed)

. The addition of Ti and Mo promoted the hardness and yield strength of the alloys, and plasticity reduced dramatically. The mixing enthalpy of Mo with Nb, Zr, and Ti was negative, and Mo had a higher melting point, resulting in component segregation. It can be demonstrated by examining UNb_0.5Zr_0.5Ti_0.5Mo_0.5, which has a higher hardness of 350 HB than that of UNb_0.5Zr_0.5Ti_0.2Mo_0.2.

4. Discussion

The researched alloys in the present article are all BCC solid solution structures, per the solid-solution formation criteria and microstructure characterization. Figure 13 shows the concept of the DUHEA design process, which begins with the ternary U-Nb-Zr system, adds Ti and Mo elements to create the quaternary alloys and, ultimately, finishes with the quinary UNb_0.5Zr_0.5Ti_xMo_y alloy. The mixing enthalpy of U with Nb, Ti, Zr, and Mo had a significant impact on the structure and mechanical properties of the studied alloys. The relationship between the mixing enthalpy and the mechanical characteristics of the alloys are presented in Figure 14. The compressive yield strength and hardness exhibited a rising trend as the mixing enthalpy fell. Though UNb_0.5Zr_0.5Ti_0.5Mo_0.5 and UNb_0.5Zr_0.5Mo had higher strength, severe component segregation microstructures resulted in poor plasticity. This was due to the melting point of Mo being higher than those of other elements, resulting in component segregation and poor performance. Finally, based on our combined theoretical and experimental results, UNb_0.5Zr_0.5Mo_0.5 and UNb_0.5Zr_0.5Ti_0.2Mo_0.2 had a homogeneous structure and outstanding mechanical characteristics.

5. Conclusions

In this paper, we examined the composition of UNb_0.5Zr_0.5Mo_0.5 and UNb_0.5Zr_0.5Ti_0.2Mo_0.2, finding both to possess a homogeneous structure, low segregation, and outstanding mechanical properties. The alloys examined were screened during the design process from the DU ternary alloy to DUHEA according to the formation law of HEAs and based on experimental results. UNb_0.5Zr_0.5Mo_0.5 and UNb_0.5Zr_0.5Ti_0.2Mo_0.2 were composed of a single BCC structure, which was in line with our theoretical calculations. The hardness and strength of UNb_0.5Zr_0.5Mo_0.5 and UNb_0.5Zr_0.5Ti_0.2Mo_0.2 were 305 HB and 1452 MPa, and 297 HB and 1157 MPa, respectively. This suggests that the HEA phase-formation criteria could have a wide range of applications in the design of DUHEAs, providing promising theoretical direction for the future development of specific BCC-structured HEAs.